This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to the problems shown in the image. Step 1: Simplify the expression using exponent rules. For problem 2, we use the power of a power rule (x^m)^n = x^mn and the quotient rule (x^m)/(x^n) = x^m-n. ((4^2)^4)/(4^8) = 4^2 × 44^8 = (4^8)/(4^8) = 4^8-8 = 4^0 = 1 The simplified expression is 1. Step 2: Simplify the expression by combining like terms. For problem 3, we use the product rule x^m × x^n = x^m+n. Remember that a = a^1 and b = b^1. a × b × a^2 × b^5 = (a^1 × a^2) × (b^1 × b^5) = a^1+2 × b^1+5 = a^3 × b^6 = a^3 b^6 The simplified expression is a^3 b^6. Step 3: Evaluate the expression. For problem 4, the expression a × 5^n is already in its simplest form. There are no further operations to perform without specific values for a or n. The expression is a × 5^n. Step 4: Evaluate the power of a fraction. For problem 5, we apply the power to both the numerator and the denominator: ((x)/(y))^n = (x^n)/(y^n). ((13)/(10))^3 = (13^3)/(10^3) Calculate the powers: 13^3 = 13 × 13 × 13 = 169 × 13 = 2197 10^3 = 10 × 10 × 10 = 1000 So, ((13)/(10))^3 = (2197)/(1000) The evaluated expression is (2197)/(1000). That's 2 down. 3 left today — send the next one.